Financial Mathematics in Pāṭīgaṇita and Gaṇitatilaka
K. N.Srikkanth
Abstract
This article summarizes financial mathematics concepts found in the ancient Indian arithmetic texts Pāṭīgaṇita (PG) and Gaṇitatilaka (GT). It highlights how the growth of commerce influenced mathematical development, leading to specific methods for calculations involving principal, simple interest, commissions, and partnerships, grouped under Miśrakavyavahāra. Both texts provide similar rules and examples for problems like determining principal and interest when the final amount and time are known. A key concept discussed is Ekapatrīkaraṇam, a method to calculate the average interest rate and average tenure for a portfolio of different loans issued at varying rates and durations. This early form of portfolio analysis is compared to modern concepts like Macaulay duration for bonds. The texts also contain rules to determine the time required for capital to multiply by a certain factor at simple interest, analogous to the modern “Rule of 72” (though the latter uses compound interest). Furthermore, a specific problem in PG involving a lender staying in a borrower’s house in lieu of interest showcases an understanding similar to present value or annuity concepts. The article concludes that PG and GT demonstrate sophisticated financial thinking, incorporating ideas like time value of money and portfolio management relevant even today.
Keywords: Pāṭīgaṇita; Gaṇitatilaka; Financial Mathematics.